# How do you find the derivative of #(e^(2*x)-e^(-2*x))/(e^(2*x)+e^(-2*x))#?

is

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of ( \frac{{e^{2x} - e^{-2x}}}{{e^{2x} + e^{-2x}}} ), you can use the quotient rule. Let ( u = e^{2x} - e^{-2x} ) and ( v = e^{2x} + e^{-2x} ). Then the derivative is given by:

[ \frac{{d}}{{dx}}\left(\frac{{u}}{{v}}\right) = \frac{{u'v - uv'}}{{v^2}} ]

where ( u' ) and ( v' ) are the derivatives of ( u ) and ( v ) with respect to ( x ), respectively.

Now, differentiate ( u = e^{2x} - e^{-2x} ) and ( v = e^{2x} + e^{-2x} ), then apply the quotient rule to find ( \frac{{du}}{{dx}} ) and ( \frac{{dv}}{{dx}} ). Afterward, substitute into the quotient rule formula to find the derivative of ( \frac{{e^{2x} - e^{-2x}}}{{e^{2x} + e^{-2x}}} ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the derivative of #P(t) = 3000 + 500 sin(2πt−(π/2))#?
- How do you implicitly differentiate #x^2 + y^2 = 1/2 #?
- How do you find the first and second derivatives of #f(x)=(x-1)/(x+1)# using the quotient rule?
- How do you find the derivative of #y = 3 / (cos2x^2)#?
- How do you differentiate #g(x) = sqrt(2x^2-1)cos3x# using the product rule?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7